CE 473/573 Groundwater
Fall 2012
Homework 6
Due Friday October 12
*36. Continue adding to our list of contemporary issues involving groundwater, but expand
to include international issues:
a. Find an article or webpage on a contemporary groundwater issue in a country
(not the U.S.) that starts with the same first letter as one of last names of your
group members. Provide the web address.
b. In a paragraph of 200 words or fewer, summarize the problem; explain the effect of
the problem or an engineering solution on the economy, environment, or society;
relate the problem or solution to the material in class; and discuss whether the
problem or solution would be different in the U.S.
c. Find an image that illustrates this problem—e.g., a photograph, map, drawing,
schematic, etc. Provide image and the link.
d. Submit your text, links, and images via email to me (so that I can compile them
easily).
37. Suppose a confined aquifer has a width that can be approximated as w = w0 exp(−αx).
The hydraulic conductivity is K, the thickness of the aquifer is b, and the heads are
h0 and hL at x = 0 and x = L, respectively.
a. Derive an expression for the flow Q in terms of these parameters.
b. Derive an expression for the head as a function of x and show that it satisfies the
case of α → 0.
c. Compute the flow and plot the head as a function of x for K = 5 m/d, b = 30 m,
w0 = 500 m, α = 8 × 10−4 m−1 , L = 1000 m, h0 = 35 m, and hL = 33 m.
d. Explain the variation of head with x physically.
38. An unconfined aquifer of length 2700 m, width 1500 m, and hydraulic conductivity
0.5 m/d lies between two reservoirs. The bottom of the aquifer is at elevation 120 m
(above some datum). The reservoir levels are at elevations of 150 m and 146 m.
a. Compute the flow between the two reservoirs.
b. Your colleague computed a flow of 329 m3 /d. What is your colleague’s mistake?
*39. In your careers you will have to review the work of others. Review the solution
(attached) to the following problem and explain the errors that the students made.
The Biscayne aquifer consists mainly of two layers: the Miami Limestone formation and the Fort Thomson formation. The hydraulic conductivity of the former is
1500 m/d, and the hydraulic conductivity of the latter is 12, 000 m/d.
a. Plot the water table.
b. Compute the flowrate per unit width.
c. Plot the effective conductivity as a function of x.
d. Repeat parts a-c if the downstream water elevation is -6 m.
1 km
Elev. 2.44 m
Elev. 1.07 m
Miami limestone formation
Elev. 1.00 m
Elev. -3.00 m
Fort Thompson formation
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Elev. -15.24 m
*40. Your supervisor asks you to design an agricultural drain system for a corn field.
Suppose the hydraulic conductivity of the soil is 5 × 10−7 m/s, the recharge rate
is 6 mm/day, the drain spacing is 10 m, the depth of the aquifer is 20 m and the root
depth is 0.8 m.
a. If the drains are to be placed at the same elevation, compute the depth from the
ground surface below which the water table will be below the roots.
b. Compute the flow per unit width into both drains and convince me that your
answer is correct.
c. Suppose the crew installing one of the drains mistakenly installed it 0.3 m deeper
than they should have. Compute the recharge rate below which no groundwater
divide will occur.
Recharge
Roots
Ground surface
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Drains
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Aquifer bottom
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L
41. Construct a numerical model of flow in a confined aquifer with thickness 10 m, length
1500 m, and hydraulic conductivity varying linearly from 1 to 5 m/d. The upgradient
head is 35 m, and the downgradient head is 34 m.
a. Plot the variation in piezometric head.
b. Compute the flow per unit width.
c. Convince me that your result in part a is correct.
d. Compute the effective conductivity.
*42. After you start working at Realenwelt Consulting, you are asked to construct a numerical model of flow in an agricultural field. The aquifer, which is next to a stream,
is unconfined and heterogeneous; the alluvium near the stream has a conductivity of
KA = 1 m/d and a effective porosity of nA = 0.3, while the soil farther from the
stream has a conductivity of Ks = 0.3 m/d and an effective porosity of ns = 0.25.
An old tile drain was installed 20 m away from the stream many years ago, but after
several years of drought, the field (but not the buffer strip) is irrigated at a rate of
5 mm/d.
a. At this irrigation rate, does any water enter the drain?
b. Fertilizer applied to the field might cause nutrients to enter the stream. The
nutrient concentration will depend on the time the water remains in the soil. Use
your numerical solution to compute the time to travel from the edge of the field to
the stream. (Hint: Apply the formula we have used between cells in your model
and add the times.)
13.5 m
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5 mm/d
Corn field
0.9 m
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Drain
Buffer
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Ks
ns
1.2 m
KA
nA
Aquifer bottom
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20 m
6m